Cheddar First School Calculation Policy
Early Learning Goal
In Reception children count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number. Using quantities
and objects, they add and subtract two single-digit numbers and count on and back to find the answer. They solve problems, including doubling, halving and sharing .
Key Stage 1
Overview of KS1
Children in Years 1 and 2 will be given a really solid foundation in the basic building blocks of mental and written arithmetic. Through strong teaching of place
value and a structured progression from beadstrings and bead bars to number lines, they will develop an understanding of how numbers work, so that they
are confident in 2-digit numbers and beginning to read and say numbers above 100. A focus on number bonds, first via practical hands-on experiences then
subsequently consolidated by the use of memorisation techniques, will enable a good grounding in these crucial facts, and ensure that children leave Y2
knowing the pairs of numbers which make all the numbers up to 10, at least. They will also have experienced and been taught pairs to 20. Their knowledge of
number facts enables them to add several single-digit numbers, and to add/subtract a single digit number to/from a 2-digit number. Another important
conceptual tool is their ability to add/subtract 1 or 10, and to understand which digit changes and why. This understanding is extended to enable children to
add and subtract multiples of ten to and from any 2-digit number. The most important application of this knowledge is their ability to add or subtract any pair
of 2-digit numbers by counting on or back in tens and ones. Children may extend this to adding by partitioning numbers into tens and ones. Children will be
taught to count in 2s, 3s, 5s and 10s, and will have related this skill to repeated addition. They will have met and begun to learn the associated 2x, 3x, 5x and
10x tables. Engaging in a practical way with the concept of repeated addition and the use of arrays enables children to develop a preliminary understanding of
multiplication, and asking them to consider how many groups of a given number make a total will introduce them to the idea of division. They will also be
taught to double and halve numbers, and will thus experience scaling up or down as a further aspect of multiplication and division. Fractions will be
introduced as numbers and as operators, specifically in relation to halves, quarters and thirds.
Mental calculation
Addition
Subtraction
Year
1
Written Calculation
Recall number bonds (‘story of’ 5, 6, 7, 8, 9 and 10)
Count on in ones from a given 2-digit number
Add two single-digit numbers
Add three single-digit numbers spotting doubles or pairs to 10
Count on in tens from any given 2-digit number
Add 10 to any given 2-digit number
Use number facts to add single-digit numbers to two-digit
numbers, e.g. Add by putting the larger number first
Understand the effect of adding zero
Use + and = in number sentences of own e.g. 5 + 0 = 5, 3 + 4 = 7, 6 + 3 = 9
Recall number bonds (‘story of’ 5, 6, 7, 8, 9 and 10)
Count back in ones from a given 2-digit number
Subtract one single-digit number from another
Count back in tens from any given 2-digit number
Subtract 10 from any given 2-digit number
Use number facts to subtract single-digit numbers from twodigit numbers.
Understand the effect of subtracting zero
Use - and = in number sentences of own e.g. 10 - 3 = 7, 8 - 5 = 3, 6 – 0 = 6
Multiplication
Begin to count in 2s, 5s and 10s
Begin to say what three 5s are by counting in 5s or what four
2s are by counting in 2s, etc.
Double numbers to 10
□
□
□
5+
= 10, 7 +
= 10, 2 +
= 10
2 + 5 + 3 = 10, 3 + 4 + 3 = 10, 5 + 1 + 5 = 1
15 + 30 = 45, 21 + 40 = 61, 37 + 20 = 57
32 + 10 = 42, 41 + 10 = 51, 15 + 10 = 25
Use 4 + 3 to work out 14 + 3 = 17, 24 + 3 = 27, 34 + 3 = 37…
□
□
□
8= 5, 6 = 4, 9 =3
60 – 20 = 40, 52 – 30 = 22, 34 – 20 =14
23 – 10 = 13, 75 – 10 = 65, 40 – 10 = 30
Use 7 – 2 to work out 17 -2 = 15, 27 – 2 = 25, 37 – 2 = 35 …
3 x 5 = 15, 4 x 2 = 8, 2 x 10 = 20
3+3=6
5 + 5 = 10
8 + 8 = 16
Division
Addition
Year
2
Begin to count in 2s, 5s and 10s
Find half of even numbers to 12 and know it is hard to halve
odd numbers
Find half of even numbers by sharing
Begin to use visual and concrete arrays or ‘sets of’ to find how
many sets of a small number make a larger number.
Number bonds – knowing all the pairs of numbers which make
all the numbers to 10, and pairs with a total of 20
Count on in ones and tens from any given 2-digit number
Add two or three single-digit numbers
Add a single-digit number to any 2-digit number using number
facts, including bridging multiples of 10.
Add 10 and small multiples of 10 to any given 2-digit number
Add near multiples of 10 to any 2-digit number
Add any pair of 2-digit numbers
Know that addition of two numbers can be done in any order
(commutative)
Use inverse relationship between addition and subtraction to
check calculations.
□ = 20, 9 + 11 = 20
3 + 17 = 20, 12 +
4 + 6 + 7 = 17, 6 + 8 + 5 = 19, 3 + 9 + 6 = 18
45 + 4 = 49, 38 + 7 = 45, 26 + 5 = 31
□
64 + 10 = 74, 27 + 30 = 57, 42 +
= 82
23 + 9 = 32, 23 + 19 = 42, 23 + 11 = 34, 23 + 21 = 44
32 + 24
= 30 + 20 + 2 + 4
= 50 + 6
= 56
Subtraction
Number bonds – knowing all the pairs of numbers which make
all the numbers to 10
Count back in ones and tens from any given 2-digit number
Subtract a single-digit number from any 2-digit number using
number facts, including bridging multiples of 10.
Subtract 10 and small multiples of 10 from any given 2-digit
number
Subtract near multiples of 10 from any 2-digit number
Subtract any pair of 2-digit numbers by counting back in tens
and ones or by counting up.
Know that subtraction of one number from another cannot be
done in any order (not commutative)
Use inverse relationship between addition and subtraction to
check calculations.
Multiplication
Count in 2s, 5s and 10s
Begin to count in 3s.
Begin to understand that multiplication is repeated addition
and to use arrays (e.g. 3 x 4 is three rows of 4 dots)
Begin to learn the 2x, 3x, 5x and 10x tables, seeing these as
‘lots of’, e.g. 5 lots of 2, 6 lots of 2, 7 lots of 2, etc.
Know that multiplication of two numbers can be done in any
order ( commutative)
Double numbers up to 20
Begin to double multiples of 5 to 100
Begin to double two-digit numbers less than 50 with 1s digits
of 1, 2, 3 4 or 5
□ = 10 etc.
7 + 3 = 10, 4 + 6 =10, 2 +
56 – 3 = 52, 48 – 5 = 43, 62 – 4 = 58 .
□ = 42
56 – 10 = 46, 32 – 20 = 12, 82 –
23 - 9 = 14, 43 - 19 = 24, 35- 11 = 24, 63 - 21 = 42
48 – 22 = 26, 65 – 23 = 42, 57 – 34 = 23 (counting back)
35 – 28 = 7, 54 – 36 = 18, 62 – 47 = 15 (counting on)
Use x and = in number sentences of own e.g 5 x 4 = 20, 8 x 10 = 80, 6 x 3 = 18
□x
5 = 15,
□x
3 = 12,
□x
10 = 60
12 + 12 = 24, 14 + 14 = 28, 16 = 16 + 32
15 + 15 = 30, 25 + 25 = 50, 35 + 35=70
23 + 23
= 20 + 20 + 3 + 3
= 40 + 6
= 46
Double 23
40
6
40 + 6 = 46
Division
Count in 2s, 5s and 10s
Begin to count in 3s
Using fingers, say where a given number is in the 2s, 5s or 10s
count. (e.g. 8 is the fourth number when I count in twos.)
Relate division to grouping. (e.g. how many groups of five in
fifteen?)
Know that division of one number from another cannot be
done in any order (not commutative)
Halve numbers to 20
Begin to halve numbers to 40 and multiples of 10 to 100
1
Find ½, /3, ¼ and ¾ of a quantity of objects and of amounts
(whole number answers)
□ = 5, 24 ÷ 3 = 8
Use ÷ and = in number sentences of own e.g. 15 ÷ 5 = 3, 50 ÷
□÷5 = 3, □÷ 3 = 4, □÷10 = 6
Halve
28
10
4
10 + 4 = 14
Lower Key Stage 2
Overview of Lower KS2
Addition
Year
3
In the Lower Juniors, children build on the concrete and conceptual understandings they have gained in years 1 and 2 to develop a real mathematical
understanding of the four operations, in particular developing arithmetical competence in relation to larger numbers. In addition and subtraction, they are
taught to use place value and number facts to add and subtract numbers mentally and will develop a range of strategies to enable them to discard the
‘counting in ones’ or fingers-based methods of the infants. In particular, they will learn to add and subtract multiples and near multiples of 10, 100 and 1000,
and will become fluent in complementary addition as an accurate means of achieving fast and accurate answers to 3-digit subtractions. Standard written
methods for adding larger numbers are taught, learned and consolidated, and written column addition and subtraction is also introduced. This key stage is
also the period during which all the multiplication and division facts are thoroughly memorised, including all facts up to the 12 x 12 table. Efficient written
methods for multiplying or dividing a 2-digit or 3-digit number by a single-digit number are taught, as are mental strategies for multiplication or division with
large but friendly numbers, e.g. when dividing by 5 or multiplying by 20. Children will develop their understanding of fractions, learning to reduce a fraction to
its simplest form as well as finding non-unit fractions of amounts and quantities. The concept of a decimal number is introduced and children consolidate a
firm understanding of one-place decimals, multiplying and dividing whole numbers by 10 and 100.
Know pairs with each total to 20
Know pairs of multiples of 10 with a total of 100
Add any two 2-digit numbers by counting on in 10s and 1s or
by using partitioning
Add multiples and near multiples of 10 and 100.
Perform place value additions without a struggle. (e.g. 300 + 8
+ 50 = 358)
Use place value and number facts to add multiples of 10 and
100 to 3-digit numbers (e.g 346 + 50, 346 + 500)
Use place value and number facts to add a 1-digit or 2-digit
number to a 3-digit number. (e.g. 104 + 56 is 160 since
104+50=154 and 6+4=10 and 676 + 8 is 684 since 8=4+4 and
76+4+4=84)
Add pairs of ‘friendly’ 3-digit numbers, e.g. 320 + 450
Begin to add amounts of money using partitioning.
Use expanded column addition to add two or three 3-digit numbers or three 2-digit numbers. e.g.
362 + 483 is
300 60 2
+ 400 80 3
700 140 5 = 845
300 60 2
+ 400 80 3
100
800 40 5
Begin to use compact column addition to add numbers with three digits.
325
+ 357
1__
7 8 2_
173
+455
1
628
Estimate and use inverse operations to check answers to a calculation
3
1
1
Begin to add like fractions. (e.g. /8 + /8 + /8)
3
2
Recognise fractions that add to 1. (e.g. ¼ + ¾ or /5 + /5)
Subtraction
Know pairs with each total to 20
Subtract any two 2-digit numbers
Perform place value subtractions without a struggle. (e.g. 536
3 =533, 536 – 30 = 506, 536 – 300 =236 etc.)
Subtract 2-digit numbers from 3-digit numbers by counting up.
(e.g. 143 – 76 is done by starting at 76, add 4 (80) then add 20
(100) then add 43 making the difference a total of 67)
Subtract multiples and near multiples of 10 and 100.
Subtract, when appropriate, by counting back or taking away,
using place value and number facts.
Find change from £1, £5 and £10.
Use counting up (complementary addition) as an informal written strategy for subtracting pairs of three-digit
numbers, e.g .423 – 357 is
+3
357
+40
360
+23
400
= 66
423
Use expanded column subtraction to subtract two or three 3-digit numbers
e.g. 485 - 53
400 80 5
+ 300 50 3
100 30 2 = 132
Estimate and use inverse operations to check answers to a calculation
7
3
Begin to subtract like fractions. (e.g. /8 - /8)
Multi plication
Know by heart all the multiplication facts in the 2x, 3x, 4x, 5x,
8x and 10x tables
Multiply whole numbers by 10 and 100
Recognise that multiplication is commutative
Use place value and number facts in mental multiplication.
(e.g. 30 x 5 is 15 x 10)
Partition teen numbers to multiply by a single-digit number.
(e.g. 3 x 14 as 3 x 10 and 3 x 4)
Double numbers up to 50
Use partitioning (grid multiplication) to multiply 2-digit numbers by ‘friendly’ single digit number, e.g. 34 x 5
X
30
4
5
150
20
Double
150 + 20 = 170
36
60
12
60 + 12 =72
Know by heart all the division facts derived from the 2x, 3x, 4x,
5x, 8x and 10x tables.
Divide whole numbers by 10 or 100 to give whole number
answers
Recognise that division is not commutative.
Use place value and number facts in mental division. (e.g. 84 ÷
4 is half of 42)
Divide larger numbers mentally by subtracting the tenth
multiple, including those with remainders. (e.g. 57 ÷ 3 is 10 + 9
as 10x3=30 and 9x3=27)
Halve even numbers to 100, halve odd numbers to 20
th
Perform divisions just above the 10 multiple using the written layout and understanding how to give a
remainder as a whole number e. g. 65 ÷ 5
Halve 76
Division
35
3
35 + 3 =38
Find unit fractions of quantities and begin to find non-unit fractions of quantities
Addition
Year
4
Add any two 2-digit numbers by partitioning or counting on
Know by heart/quickly derive number bonds to 100 and to £1
Add to the next hundred, pound and whole number. (e.g. 234
+ 66 = 300, 3.4 + 0.6 = 4)
Perform place value additions without a struggle. (e.g. 300 + 8
+ 50 + 4000 = 4358)
Add multiples and near multiples of 10, 100 and 1000.
Add £1, 10p, 1p to amounts of money
Use place value and number facts to add 1-, 2-, 3-and 4-digit
numbers where a mental calculation is appropriate’. (e.g. 4004
+ 156 by knowing that 6+4=10 and that 4004+150= 4154 so
total is 4160)
Use expanded then compact column addition for 3-digit and 4-digit numbers, including money.
425
+ 357
1__
7 8 2_
+
£ 4. 2 5
£ 3 .5 7
.1__
£ 7. 8 2
3 6 8 7
+ 4 2 5 6
1 1__
7 9 4 3
Estimate and use inverse operations to check answers to a calculation
3
4
7
2
Add like fractions, e.g. /5 + /5 = /5 = 1 /5.
2
Be confident with fractions that add to 1 and fraction complements to 1. (e.g. /3 + ? = 1)
Subtract any two 2-digit numbers
Know by heart/quickly derive number bonds to 100
Perform place value subtractions without a struggle. (e.g. 4736
– 706 = 4030, etc.)
Subtract multiples and near multiples of 10, 100 and 100
Subtract by counting up. (e.g. 503 – 368 is done by adding: 368
+2 +30 +100 +3 so we added 135)
Subtract, when appropriate, by counting back or taking away,
using place value and number facts.
Subtract £1, 10p, 1p from amounts of money
Find change from £10, £20 and £50.
Use expanded then compact column subtraction for 3-digit and 4-digit numbers.
40 11
600 50 1
-- 300 20 4
300 20 7
4 11
651
--3 2 4
3 27
3000 1600 40 11
4000 600 50 1
-- 1000 800 20 4
2000 800 20 7
3 16 4 11
4651
-- 1 8 2 4
2827
Subtraction
Use complementary addition to subtract amounts of money, and for subtractions where the larger number
is a near multiple of 1000 or 100 ( involves a zero)
E.g. 2002 – 1865 is
+5
+30
+102
= 137
1865 1870
1900
2002
Estimate and use inverse operations to check answers to a calculation
1
3
Subtract like fractions, e.g. ¼ + /8 = /8
2
1
Use fractions that add to 1 to find fraction complements to 1, e.g. 1 – /3 = /3
Multiplication
Know by heart all the multiplication facts up to 12 x 12.
Recognise factors up to 12 of two-digit numbers.
Multiply three numbers together e.g.6 x 5 x 4
Multiply whole numbers and one-place decimals by 10, 100,
1000
Multiply multiples of 10, 100, 1000 by single digit numbers.
(e.g. 300 x 6 or 4000 x 8)
Use understanding of place value and number facts in mental
multiplication. (E.g. 36 x 5 is half of 36 x 10 and 50 x 60 = 3000)
Partition 2-digit numbers to multiply by a single-digit number
mentally. (e.g. 4 x 24 as 4 x 20 and 4 x 4)
Multiply near multiples using rounding. (e.g. 33 x 19 as 33 x 20
– 33)
Find doubles to double 100 and beyond using partitioning
Begin to double amounts of money. (e.g. £35.60 doubled =
£71.20.)
Use partitioning (grid multiplication) to multiply 2-digit and 3-digit numbers by any single digit number, e.g.
38 x 57 or 634 x 9
X
9
600
30
4
5 400
270
36
5400 + 270 + 36 = 5 706
Use an expanded vertical written method to multiply a one-digit by a 3-digit number e.g 314 x 3 (ladder)
Then move to a compact written method.
X
314
3
1 2 (3 x 4)
3 0 (3 x10)
9 0 0 (3 x 300)
____
942
3 1 4
X
3
___ 1__
9 4 2
Division
Know by heart all the division facts up to 144 ÷ 12.
Divide 1 or 2-digit whole numbers by 10, 100 to give whole
number answers or answers with one or two decimal places
Divide multiples of 100 by 1-digit numbers using division facts.
(e.g. 3200 ÷ 8 = 400)
Use place value and number facts in mental division. (e.g. 245
÷ 20 is double 245 ÷ 10 )
th
th
Divide larger numbers mentally by subtracting the 10 or 20
multiple as appropriate. (e.g. 156 ÷ 6 is 20 + 6 as 20x6=120 and
6x6=36)
Find halves of even numbers to 200 and beyond using
partitioning
Begin to halve amounts of money. (e.g. Half of £52.40 =
£26.20)
th
Perform divisions just above the 10 multiple using the written layout and understanding how to give a
remainder as a whole number e. g. 65 ÷ 5, 69 ÷5
Use an expanded written method to divide a 2-digit or a 3-digit number by a single-digit number, e.g.44 ÷ 3
1 4 rem 2
3
) 44
-- 3 0 (10 x 3)
14
-- 1 2 (4 x 3 )
2
Give remainders as whole numbers.
Begin to reduce fractions to their simplest forms.
Find unit and non-unit fractions of larger amounts.
2 2 rem 4
6) 136
-- 1 2 0 ( 20 x 6)
16
-- 1 2 ( 2 x 6)
4